Timeline for Diffeomorphisms fixing origin and boundary
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Apr 26, 2020 at 8:59 | comment | added | Greg Friedman | @ThomasRot Independent of the original question, that looks like an interesting book. Thanks for posting a link. | |
| Apr 22, 2020 at 22:07 | comment | added | Daniele Zuddas | you are all right! thanks, I remove my comment | |
| Apr 22, 2020 at 16:15 | comment | added | Igor Belegradek | As others say the diffeomorphism group of $D^n$ rel boundary is complicated, see e.g. pi.math.cornell.edu/~hatcher/Papers/Diff%28M%292012.pdf. | |
| Apr 22, 2020 at 14:02 | comment | added | Ryan Budney | They are not all isotopic to the identity. Roughly speaking in high dimensions there is a bijection between these isotopy classes and the group of exotic $(n+1)$-spheres. Getting back to the original question, what kind of characterization do you want? You could view the homotopy-type of these diffeomorphism groups as the "generators" of the difference between the categories of topological and smooth manifolds. | |
| Apr 22, 2020 at 12:10 | history | edited | Thomas Rot |
added tag
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| Apr 22, 2020 at 12:04 | comment | added | Thomas Rot | people.math.harvard.edu/~kupers/teaching/272x/book.pdf | |
| Apr 22, 2020 at 12:04 | comment | added | Thomas Rot | And I would guess the map $\mathrm{Diff}_\partial (D^n)\rightarrow \mathrm{int}(D^n)$ that sends a diffeomorphism that preserves the boundary to its evaluation at $0$ is a fibration with fiber the space in the OP. That would mean that the homotopy groups are the same. | |
| Apr 22, 2020 at 11:54 | comment | added | Thomas Rot | @DanieleZuddas: Is that really true? How to see that? The number of connected components of the space of all diffeomorphisms fixing the boundary (but not the origin) is pretty complicated. | |
| Apr 22, 2020 at 9:55 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Apr 22, 2020 at 9:50 | history | asked | ABIM | CC BY-SA 4.0 |